principal_axes_inertia
Transform the inertia tensor \(\boldsymbol{j}_a\) defined about the A frame of reference to the centre of
gravity and aligned with the principal axes of inertia.
The inertia tensor about the centre of gravity is obtained using the parallel axes theorem
\[\boldsymbol{j}_{cm} = \boldsymbol{j}_a + \tilde{r}_{cg}\tilde{r}_{cg}m\]
and rotated such that it is aligned with its eigenvectors and thus represents the inertia tensor about the principal axes of inertia
\[\boldsymbol{j}_p = T_{pa}^\top \boldsymbol{j}_{cm} T^{pa}\]
where \(T^{pa}\) is the transformation matrix from the A frame to the principal axes P frame.
- param j_a:
Inertia tensor defined about the
Aframe.- type j_a:
np.array
- param r_cg:
Centre of gravity position defined in
Acoordinates.- type r_cg:
np.array
- param m:
Mass.
- type m:
float
- returns:
Containing \(\boldsymbol{j}_p\) and \(T^{pa}\)
- rtype:
tuple